101 Things Everyone Should Know About Math by Marc Zev & Kevin B. Segal & Nathan Levy

Author:Marc Zev & Kevin B. Segal & Nathan Levy
Language: eng
Format: epub
ISBN: 9780970010636
Publisher: Science, Naturally!

Their agent has lined up two possible gigs for them on Saturday night. One is at the City A Auditorium, pays $200, and is 15 miles away. The second possible gig is at the City B Bistro, pays $300, and is 150 miles away. Take into account that the agent will get 10% of the fee off the top (meaning they have to pay their agent first before expenses) and consider that gas costs $3 a gallon.

Which gig will be a better deal for the June Bugs?

The answer is: The City B Bistro

They make $200 from the City A gig.

• First, $20 ($200 x 0.1) goes to the agent.

• Then figure how much the gas costs for the round trip. $3 x (2 x 15mi) ÷ 15mpg = $6 for gas.

• That leaves $174.

They make $300 from the City B gig

• First, $30 ($300 x 0.1) goes to the agent.

• $3 x (2 x 150mi) ÷ 15mpg = $60 goes to gas.

• That leaves $210.

42. Around the World

When Ferdinand Magellan set off to be the first to circumnavigate the world, he requested that each ship in his expedition carry 18 hourglasses.

Magellan’s plan was for some of the hourglasses to run for 30 minutes, some to run for one hour, some to run for two hours, and some to run for four hours. All of the hourglasses were the same size, but each had different amounts of sand to measure the time.

Imagine that the hourglasses were made by making two empty cones out of glass and connecting them point to point. In order for the sand to flow correctly, the sand needed to come up to a height of at least 2-inches, but not more than ¾ the length of the cone.

What is the minimum height of each of the cones?

E. 3 inches

F. 4¹/₂ inches

G. 5¹/₃ inches

H. 7 inches

NEED A CLUE? Imagine putting some arbitrary amount of sand in one (point down) cone. We can say that the height the sand reaches is H, and the volume of the sand as V. Now picture adding sand so that the height of the sand is doubled to 2H, resulting in a volume that can be expressed as 23V or 8V.

The answer is: G, 5⅓ inches

Reminder: The formula for the volume of a cone (V) is:

V= ⅓∏r2h

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